Cell structures Quadrilateral grid geometry
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direct position X within the grid cell U bounded by the solid lines will be based on interpolation from a, b, c and d and possibly involve additional grid points outside the cell.
In this International Standard, the term grid cell refers to the cell bounded by the grid lines that connect the grid points. The term sample space refers to the observed or measured space surrounding a sample point.
The term footprint refers to a representation of a sample space in the context of some coordinate reference system.
In dealing with gridded data, e.g. for processing or portrayal, it is often assumed that the size and shape of the sample spaces are a simple function of the spatial distribution of the sample points, and that the grid cells and
the sample cells are congruent.
In fact, the size and shape of the sample space are determined by the method used to measure or calculate the attribute value. In the simplest case, the sample space is the sample point. It is often a disc, a sphere, or a
hypersphere surrounding the sample point. In the case of sensed data, the size and shape of the sample space is also a function of the sensor model and its position relative to the sample point, and may be quite
complex. Adjacent sample spaces may be coterminous or they may overlap or underlap.
In addition to affecting the size and shape of the sample space, the measurement technique affects the applicability of the observed or measured value to the sample space. It is often assumed that the recorded
value represents the mean value for the sample space. In fact, elements of the sample space may not contribute uniformly to the result, so that it is better conceived as a weighted average where the weighting is a
function of position within the sample space. Interpolation methods may be designed specifically to deal with characteristics of the sample space.
Transformation e.g. rectification between grid coordinates and an external coordinate reference system may distort the representation of the sample space in a way that causes interpolation errors.